It from Qubit:

Simons Collaboration on

Quantum Fields, Gravity, and Information

Frontiers of Physics

short distance long distance complexity

Higgs boson

Neutrino masses

Supersymmetry

Quantum gravity

String theory

Large scale structure

Cosmic microwave

background

Dark matter

Dark energy

“More is different”

Many-body entanglement

Phases of quantum

matter

Quantum computing

Emergent geometry

hep-th papers with “entanglement” in the title

Year (projected)

Quantum entanglement

Nearly all the information in a typical entangled “quantum book” is encoded in the correlations among the “pages”.

You can't access the information if you read the book one page at a time.

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….….

Classically Easy

Quantumly Hard

Quantumly Easy

Problems

What’s in

here?

EnvironmentDecoherence

ERROR!

To resist decoherence, we must prevent the environment from “learning” about the state of the quantum computer during the computation.

Quantum

Computer

Quantum error correction

The protected “logical” quantum information is encoded in a highly entangled state of many physical qubits.

The environment can't access this information if it interacts locally with the protected system.

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….….

Environment

Five Big Questions

1) Does spacetime emerge from entanglement?

2) Do black holes have interiors? Does the universe

exist outside our horizon?

3) What is the information-theoretic structure of

quantum field theories?

4) Can quantum computers simulate all physical

phenomena?

5) How does quantum information flow in time?

PARADOX!

Planck

1900

Hawking

1975

“The ultraviolet catastrophe”

In thermal equilibrium at nonzero temperature, the elelctromagneticfield carries an infinite energy per unit volume …

The end of

classical physics!

When the theories we use to describe Nature lead to unacceptable or self-contradictory conclusions, we are faced with a great challenges and great opportunities….

“The information loss puzzle”

The radiation emitted by an evaporating black hole is featureless, revealing nothing about how the black hole formed …

The end of quantum physics?

(Or of relativistic causality?)

event horizon

singularity

outgoing radiation

collapsing body

Information Puzzle: Is a black hole a quantum cloner?

“time slice”If information escapes from

the black hole, then ..

The same (quantum)

information is in two places

at the same time!

We’re stuck:

Either information is

destroyed or cloning

occurs. Either way, quantum physics needs revision.

time(outsidehorizon)

event horizon

singularity

time(outsidehorizon)

outgoing radiation

collapsing body

“Black hole complementarity”

“time slice”The inside and the outside

are not two separate systems.

Rather, they are two different

ways of looking at the samesystem. [Susskind 1993].

in out≠ ⊗H H H

Alice Bob

An old black hole scrambles information and reveals it quickly.

Black holes as mirrors

( )logS S S

t O r r∆ =

But not quite quickly enough for Alice to verify that the

quantum information is in two places at once (both inside and

outside the black hole). [Hayden-Preskill 2007, Susskind-Sekino 2008].

A black hole in a bottle

We can describe the formation and

evaporation of a black hole using an

“ordinary” quantum theory on the walls of

the bottle, where information has nowhere

to hide [Maldacena 1997].

A concrete realization of the “holographic

principle” [Susskind 1994].

time

CFTAdS

So at least in the one case where we think we understand

how quantum gravity works, a black hole seems not to

destroy information!

Even so, the mechanism by which information can escape

from behind a putative event horizon remains murky.

Black hole complementarity challenged

Three reasonable beliefs, not all true!

[Almheiri, Marolf, Polchinski, Sully (AMPS) 2012, Mathur 2009, Braunstein

2009]:

(1) The black hole “scrambles” information, but does not

destroy it.

(2) An observer who falls through the black hole horizon sees

nothing unusual (at least for a while).

(3) An observer who stays outside the black hole sees

nothing unusual.

“Conservative” resolution:

A “firewall” at the horizon,

rather than (2).

Classical correlations are polygamous

Betty

Adam Charlie

Quantum correlations are monogamous

unentangledfully

entangled

Betty

Adam Charlie

Quantum correlations are monogamous

fully

entangledunentangled

Betty

Adam Charlie

Monogamy is frustrating!

unentangledfully

entangled

cryptography

quantum matter

black holes

Betty

Adam Charlie

event horizon

singularity

time(outsidehorizon)

outgoing radiation

Complementarity Challenged

Betty Adam

Charlie

(1) For an old black hole, recently

emitted radiation (B) is highly

entangled with radiation

emitted earlier (C) by the time it

reaches Charlie.

(2) If freely falling observer sees

vacuum at the horizon, then the

recently emitted radiation (B) is

highly entangled with modes

behind the horizon (A).

(3) If B is entangled with C by the

time it reaches Charlie, it was

already entangled with C at the

time of emission from the black

hole.

Monogamy of entanglement violated!

B A

C

AMPS experiment

singularity

time

Now a single infalling agent,

when still a safe distance

from the singularity, can be

informed that both the AB

and BC entanglement have

been confirmed, hence

verifying a violation of the

monogamy of entanglement.

rad

ius =

0

A B

C

What’s inside a black hole?

A. An unlimited amount of stuff.

B. Nothing at all.

C. Some of the same stuff that is also

outside the black hole.

D. None of the above.

Do black holes have interiors?

Does the universe exist outside

our horizon?

What is the information-theoretic

structure of quantum field theories?

(Entanglement) Entropy = Area

Bekenstein bound [Casini 2008]

Renormalization group flow [Casini-Huerta 2004, Myers 2011]

Topological order [Kitaev-Preskill 2006]

Does spacetime emerge

from entanglement?

Holographic entanglement entropy

bulk

boundary

minimal

bulk

surface

To compute entropy of region A

in the boundary field theory, find

minimal area of the bulk surface

with the same boundary:

Ryu-Takayanagi 2006

1min area(m

4) )(

m A

NG

S A ∂ =∂= +⋯

Elaborated by Headrick, Casini, Myers, Hayden, Maloney,

Balasubramanian, Marolf, Maldacena, Van Raamsdonk

Strong subadditivity from holography

boundary

[Headrick-Takayanagi 2007]

minimal

bulk

surface

bulk bulk

boundary

S(A) + S(B) ≥ S(A∩B) + S(AUB)

Nonpositive Tripartite Info: I(A;B) + I(A;C) ≤ I(A;BC)

Monogamy of mutual information (for disjoint A, B, C). True for

holographic theories, not in general. Hayden-Headrick-Maloney 2011

Building spacetime from quantum entanglement

/2i

E

i

eβ−∑ /2

| |iE

i i

i

e E Eβ− ⟩⊗ ⟩∑

A connected geometry is constructed as a superposition of disconnected geometries. The entangled state becomes a product state as the neck pinches off and the geometry becomes disconnected. [Maldacena 2003, Van Raamsdonk 2010, Maldacena-Susskind 2013].

L R

L R

L R

Alice Bob

singularity

Alice and Bob are in different galaxies, but each lives near a black hole, and their black holes are connected by a wormhole. If both jump into their black holes, they can enjoy each other’s company for a while before meeting a tragic end.

Love in a wormhole throat

time

Is spacetime a quantum error-correcting code?

Local “logical” operators in the bulk

mapped to “physical” operators on the

boundary which are well protected

against erasure of boundary degrees of

freedom. [Pastawski-Yoshida-Harlow-

Preskill 2015]

Bulk operators in the “entanglement

wedge” of (disconnected) boundary

region A can be reconstructed on A.

[Headrick et al. 2014]

erased regions

Can quantum computers simulate

all physical phenomena?

Can quantum computers simulate

all physical phenomena?

Both YES and NO are

very interesting answers!

Quantum algorithms for quantum field theories

Classical methods have limited

precision, particularly at strong

coupling.

Can a quantum computer simulate particle collisions, even at

high energy and strong coupling, using resources (number of

qubits and gates) scaling polynomially with precision, energy, and number of particles? [Jordan-Lee-Preskill 2012, 2014]

Challenges: State preparation, scaling with cutoff, massless

particles, gauge theories, …

What about quantum gravity?

Bulk physics in AdS, Matrix Models, …

What is String Theory?

U.-J. Wiese, Toward Quantum Simulating QCD (2014)

How does quantum

information flow in time?

What is time?

What is time?

Extensions of entanglement theory [Horodecki-Oppenheim 2013]

Beyond thermodynamics: “fluid dynamics” of entanglement.

Five Big Questions

1) Does spacetime emerge from entanglement?

2) Do black holes have interiors? Does the universe

exist outside our horizon?

3) What is the information-theoretic structure of

quantum field theories?

4) Can quantum computers simulate all physical

phenomena?

5) How does quantum information flow in time?

All interconnected!

Ooguri: I see that this new joint activity between quantum

gravity and quantum information theory has become very

exciting. Clearly entanglement must have something to say

about the emergence of spacetime in this context.

Witten: I hope so. I’m afraid it’s hard to work on, so in fact I’ve

worked with more familiar kinds of questions.

Kavli IPMU News

December 2014

Notices of AMS

May 2015

“Now is the time for

quantum information scientists

to jump into .. black holes”Beni Yoshida

QuantumFrontiers.comMarch 2015